Wednesday, August 26, 2009
Wednesday Math, Vol. 85: Carl Friedrich Gauss, Genius And Jerk
In the book Men of Mathematics, author E.T. Bell begins the chapter on Carl Friedrich Gauss with this sentence. "Archimedes, Newton and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit."
That's an interesting list. Bell first published in 1937, and now, more than seven decades later, the general consensus on the great mathematicians, puts at least four people that category, including my close personal mathematical bud Leonhard Euler, and there are those who would also add names from the era after Gauss like David Hilbert, Henri Poincaré, John Von Neumann and Andrey Kolmogorov.
Where did the original list of three come from?
Well, hypothetical question asker, it came from... Carl Friedrich Gauss, indirectly.
Gauss said the three greatest mathematicians were Archimedes, Newton and Eisenstein. No, not Einstein, Eisenstein. (Einstein wasn't born until a generation after Gauss' death.) Eisenstein was one of Gauss' pupils late in the great man's life, and Eisenstein's first work is on elliptic curves, an important field to this day. But Eisenstein died young, so most mathematicians today wouldn't put him in the top three, and probably not even in the top ten. The list got changed over time, Eisenstein's name erased and his better known mentor's name put in his place.
It sounds modest of Gauss to give so much credit to Eisenstein, but I think he really wanted to put his own name on the list, but was slightly embarrassed to do so. Gauss belongs there, no doubt, but I subscribe to him these ulterior motives because Gauss was a dick.
I mean, not at Superman levels of dickishness, but for a real person, there are a lot of stories from his life that show very dickish tendencies.
Here's one from his early life. In early 1801, a Sicilian astronomer named Giuseppe Piazzi saw a dwarf planet through his telescope, about half the radius of Pluto but in a much closer orbit, and tracked the object's movement for about forty days. He named the rock after Ceres, the Roman goddess who was the favored protectress of Sicily back in the day. But after forty days, Piazzi lost track of Ceres and couldn't get it back in sight.
Into the story comes 24 year old Gauss. With a remarkable insight, he realizes that the few sightings made by Piazzi could be used to predict where Ceres should be, but the method to make good on the prediction would take solving a system of seventeen equations in seventeen variables. And so, he does it, and he sends his results off to some German astronomers, who re-locate Ceres in late 1801, and Gauss is an international celebrity.
When people ask how he made his prediction, he wouldn't tell them. Some accused him of sorcery. Clearly, this was a more superstitious time. Someone should have accused him of dickery.
Okay, that's young Gauss. How about old Gauss? Well, hypothetical, he's still a genius and still a jerk.
You might dimly remember from geometry class that Euclid starts his work with five postulates. The fifth postulate, known as the parallel hypothesis, could not be proven as a theorem, though many people tried throughout history. Its statement, that there is exactly one parallel line to a given line that passes through a given point not on the line, is so intuitive that the great German philosopher Immanuel Kant makes a proclamation that it must be true, largely because Kant is so super smart and he is willing to hold his breath until his face turns blue if anyone disagrees with him. Other mathematicians slightly better than Kant work at creating a geometry where the fifth postulate isn't true, including Farkas Bolyai, a student of Gauss', who passes on his obsession to his son, János. It's János who makes the progress that finds a consistent system, meaning no internal contradictions, where the parallel postulate does not hold, the first breakthrough step in creating the field now known as non Euclidean geometry. Farkas is so proud of his son that he sends the younger man's work to his old professor Gauss. Gauss writes back that he already knew everything János wrote and that it was kind of obvious.
There are two catches here. Non Euclidean geometry may have been kind of obvious to Gauss, but Gauss is a freaking genius. Even I don't deny this. I am here to proclaim his jerkitude, but I'm not idiot enough to say it cancels out his massive smart guy-ness. The second catch is that Gauss may have known this, but he never published it. He had made the decision that he didn't want to get into a pissing match with the ghost of Immanuel Kant, who was still a big damn deal in the world of German intellectual thought.
Let me conclude by saying that any list of great mathematicians that leaves off Gauss is clearly incomplete. But as I hear more stories from the great man's life, I become more and more convinced that I will never have a man crush on Gauss the way I love Lenny Euler.
That's just the way I roll.